In a digital video signal, each sample, i.e. pixel component, is represented by an integer or floating point value. A display, such as screen, TV or monitor, that renders the video omits optical lights based on the digital values of the video signal. The function that translates the digital value V to optical light Y is the Electro-Optical-Transfer-Function (EOTF). Traditionally the EOTF has been expressed as an exponential function called a gamma function where the gamma γ is the exponent value. This is typically 2.4 (but can also be other values): Y=Vγ.
Using a gamma function works well for low luminance signals but when the luminance goes above 100 nits (cd/m2) the gamma function is not well aligned with the contrast sensitivity of the human visual system. Therefore transfer functions that are more non-linear are defined, e.g.:
                              Y          =                                                    L                p                            ⁡                              (                                                      max                    ⁡                                          [                                                                        (                                                                                    V                                                              1                                /                                m                                                                                      -                                                          c                              1                                                                                )                                                ,                        0                                            ]                                                                                                  c                      2                                        -                                                                  c                        3                                            ⁢                                              V                                                  1                          /                          m                                                                                                                    )                                                    1              /              n                                      ⁢                                  ⁢                  n          =                                                    2610                4096                            ×                              1                4                                      ≈            0.15930176                          ⁢                                  ⁢                  m          =                                                    2523                4096                            ×              128                        =            78.84375                          ⁢                                  ⁢                              c            1                    =                                                    c                3                            -                              c                2                            +              1                        =                                          3424                4096                            =              0.8359375                                      ⁢                                  ⁢                              c            2                    =                                                    2413                4096                            ×              32                        =            18.8515625                          ⁢                                  ⁢                              c            3                    =                                                    2392                4096                            ×              32                        =            18.6875                          ⁢                                  ⁢                              L            p                    =                      10000            ⁢                          cd                              m                2                                                                        [        1        ]            
This transfer function is more non-linear than the gamma function in the sense that the maximum value of its first derivative over the range from 0 to 1 is larger than that of the gamma function.
Chroma subsampling is typically done before compression as an initial step to reduce the amount of data. In 4:2:2 the chroma signal is reduced to half the resolution in the vertical direction. In 4:2:0 the chroma signal is reduced to half the resolution in both the vertical direction and the horizontal direction. This is typically done with some filtering operation to get a good quality signal but can also be done using nearest neighbor.
In order to display a 4:2:0 or 4:2:2 video, a decoder performs upsampling of the chroma signal, which can be done using bilinear filters or longer filters.
However, a combination of a highly non-linear transfer function, 4:2:0 or 4:2:2 subsampling and non-constant luminance ordering gives rise to severe artifacts to the video data, in particular for saturated colors, i.e. colors close to the color gamut edge.
There are several ways to get around this problem. One ways is to not use 4:2:0 or 4:2:2 subsampling, but use 4:4:4 instead. That, however, is expensive, since 4:2:0 halves the number of bits prior to compression, whereas 4:2:2 reduces the number of bits to two-thirds. Another way is to not use a highly non-linear transfer function. However, that means that it is hard to represent content of very high peak brightness without having banding in dark regions. A third way is to use constant luminance, i.e. apply the transfer function after conversion to the CIE1931 XYZ color space. However, such a solution is not aligned with common practice within the broadcasting industry and might in some scenarios be difficult and expensive to realize.